The closing price for XYZ Company's common stock is uniformly distributed between $10 and $20 per share.
What is the probability that the stock price will be greater than $17?
What is the probability that the stock price will be between $12.50 and $16?
To find the probability that the stock price will be greater than $17, we need to calculate the area under the probability distribution curve that represents prices greater than $17. Since the closing price is uniformly distributed between $10 and $20, we first need to determine the total area under the curve, which is equal to 1 (or 100%).
The range of prices ($10 to $20) represents the entire area under the curve, which is a rectangle. The width of this rectangle is equal to the difference between the upper and lower price limits, which is $20 - $10 = $10. The height of the rectangle is equal to the probability density function, which is 1 divided by the width, or 1/10 = 0.1. Therefore, the total area is equal to the width multiplied by the height, or 10 * 0.1 = 1.
To find the probability that the stock price will be greater than $17, we need to calculate the area under the curve for prices greater than $17. This is equal to the difference between the total area (1) and the area for prices up to $17. The area for prices up to $17 is equal to the width of the rectangle (10) multiplied by the height for prices up to $17, which is 0.1. Therefore, the area for prices up to $17 is equal to 10 * 0.1 = 1.
Since the total area is 1 and the area for prices up to $17 is also 1, the area for prices greater than $17 is 1 - 1 = 0. This means that the probability of the stock price being greater than $17 is 0, or 0%.
Now let's find the probability that the stock price will be between $12.50 and $16. To do this, we need to calculate the area under the curve for prices between $12.50 and $16. We can follow a similar process as before.
The area for prices between $12.50 and $16 is equal to the width of the rectangle (10) multiplied by the height for prices between $12.50 and $16, which is 0.1. Therefore, the area for prices between $12.50 and $16 is equal to 10 * 0.1 = 1.
Since the total area is 1 and the area for prices between $12.50 and $16 is also 1, we can conclude that the probability of the stock price being between $12.50 and $16 is 1, or 100%.